scholarly journals Coefficient Estimate of Biunivalent Functions of Complex Order Associated with the Hohlov Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Z. Peng ◽  
G. Murugusundaramoorthy ◽  
T. Janani
Keyword(s):  
Unit Disk ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimate ◽  
Complex Order

We introduce and investigate a new subclass of the function class Σ of biunivalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in this new subclass. Several, known or new, consequences of the results are also pointed out.

scholarly journals Second Hankel determinant for certain class of bi-univalent functions defined by Chebyshev polynomials

2019 ◽  
Vol 12 (02) ◽  
pp. 1950017
Author(s):  
H. Orhan ◽  
N. Magesh ◽  
V. K. Balaji
Keyword(s):  
Unit Disk ◽  
Upper Bound ◽  
Chebyshev Polynomials ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
Upper Bound Estimate

In this work, we obtain an upper bound estimate for the second Hankel determinant of a subclass [Formula: see text] of analytic bi-univalent function class [Formula: see text] which is associated with Chebyshev polynomials in the open unit disk.

scholarly journals On Some Subclasses of $m$-fold Symmetric Bi-univalent Functions associated with the Sakaguchi Type Functions

2021 ◽  
pp. 1-15
Author(s):  
Ismaila O. Ibrahim ◽  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk

In the present investigation, we introduce the subclasses $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\phi,\upsilon)$ and $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\gamma,\upsilon)$ of $m$-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the Sakaguchi type of functions and defined in the open unit disk. Further, we obtain estimates on the initial coefficients $b_{m+1}$ and $b_{2m+1}$ for the functions of these subclasses and find out connections with some of the familiar classes.

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

Estimates on Initial Coefficients of Certain Subclasses of Bi-Univalent Functions Associated with Al-Oboudi Differential Operator

2017 ◽  
Vol 84 (1-2) ◽  
pp. 73
Author(s):  
Amol B. Patil ◽  
Uday H. Naik
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk

In the present investigation we introduce two subclasses Ν<sub>Σ</sub><sup>δ</sup>,<sup>μ</sup> [η, α, λ] and Ν<sub>Σ</sub><sup>δ</sup>,<sup>μ</sup> (η, β, λ) of the function class Σ of bi-univalent functions defined in the open unit disk. These subclasses are defined by using the Al-Oboudi differential operator, which is the generalized Salagean's differential operator. Also we find estimates on initial coeffcients |a<sub>2</sub>| and |a<sub>3</sub>| for the functions in these subclasses and consider some related subclasses in connection with these subclasses.

scholarly journals On coefficient inequalities of certain subclasses of bi-univalent functions involving the Sălăgean operator

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1305-1313
Author(s):  
Amol Patil ◽  
Uday Naik
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Coefficient Inequalities

In the present investigation, with motivation from the pioneering work of Srivastava et al. [28], which in recent years actually revived the study of analytic and bi-univalent functions, we introduce the subclasses T*?(n,?) and T?(n,?) of analytic and bi-univalent function class ? defined in the open unit disk U = {z ? C : |z| < 1g and involving the S?l?gean derivative operator Dn. Moreover, we derive estimates on the initial coefficients |a2| and |a3| for functions in these subclasses and pointed out connections with some earlier known results.

scholarly journals Some general coefficient estimates for a new class of analytic and bi-univalent functions defined by a linear combination

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1313-1322 ◽  
Author(s):  
H.M. Srivastava ◽  
Müge Sakar ◽  
Güney Özlem
Keyword(s):  
Linear Combination ◽  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Faber Polynomials ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
New Class

In the present paper, we introduce and investigate a new class of analytic and bi-univalent functions f (z) in the open unit disk U. For this purpose, we make use of a linear combination of the following three functions: f(z)/z, f'(z) and z f''(z) for a function belonging to the normalized univalent function class S. By applying the technique involving the Faber polynomials, we determine estimates for the general Taylor-Maclaurin coefficient of functions belonging to the analytic and bi-univalent function class which we have introduced here. We also demonstrate the not-too-obvious behaviour of the first two Taylor-Maclaurin coefficients of such functions.

scholarly journals Coefficient bounds for a certain class of analytic and bi-univalent functions

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1839-1845 ◽  
Author(s):  
H.M. Srivastava ◽  
Sevtap Eker ◽  
Rosihan Alic
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
Recent Developments ◽  
Polynomial Expansions

In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk U. By using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class. Some interesting recent developments involving other subclasses of analytic and bi-univalent functions are also briefly mentioned.

scholarly journals Coefficient estimate of p-valent Bazilevic functions with a bounded positive real part

2015 ◽  
Vol 34 (2) ◽  
pp. 63-73
Author(s):  
O. S. Babu ◽  
C. Selvaraj ◽  
S. Logu ◽  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Unit Disk ◽  
Positive Real Part ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimate ◽  
Positive Real ◽  
Strip Domain ◽  
Bazilevic Functions ◽  
Bounded Positive Real Part

By considering a $p-$valent Bazilevi\v{c} function in the open unit disk$\triangle$ which maps $\triangle$ onto the strip domain $w$ with$p\alpha < \Re\, w < p \beta,$ we estimate bounds of coefficients and solve Fekete-Szeg\"{o} problem forfunctions in this class.\\

COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH HORADAM POLYNOMIAL

2020 ◽  
Vol 9 (12) ◽  
pp. 10091-10102
Author(s):  
D. Kavitha ◽  
K. Dhanalakshmi ◽  
N. Arulmozhi
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Univalent Function ◽  
Analytic Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
The Novel ◽  
Coefficient Estimates

In this present article, we studied and examined the novel general subclasses of the function class $\Sigma$ of bi-univalent function defined in the open unit disk, which are associated with the Horadam polynomial. This study locates estimates on the Taylor - Maclaurin coefficients $|a_{2}|$ {\it and} $|a_{3}|$ in functions of the class which are considered. Additionally, Fekete-Szeg\"{o} inequality of functions belonging to this subclasses are also obtained.

scholarly journals Third-Order Hankel Determinant for Certain Class of Analytic Functions Related with Exponential Function

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 501 ◽  
Author(s):  
Hai-Yan Zhang ◽  
Huo Tang ◽  
Xiao-Meng Niu
Keyword(s):  
Unit Disk ◽  
Exponential Function ◽  
Upper Bound ◽  
Analytic Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Third Order ◽  
The Third

Let S l * denote the class of analytic functions f in the open unit disk D = { z : | z | < 1 } normalized by f ( 0 ) = f ′ ( 0 ) − 1 = 0 , which is subordinate to exponential function, z f ′ ( z ) f ( z ) ≺ e z ( z ∈ D ) . In this paper, we aim to investigate the third-order Hankel determinant H 3 ( 1 ) for this function class S l * associated with exponential function and obtain the upper bound of the determinant H 3 ( 1 ) . Meanwhile, we give two examples to illustrate the results obtained.

Sign in / Sign up

Export Citation Format

Share Document